Abstract

We consider projective spaces constructed over (real or complex) matrix rings and study their topological separation properties. The method of construction results in non-Hausdorff spaces, where incidence properties associated with a Grassmann/flag interpretation of the spaces are neatly encoded in the lack of standard topological separation properties. The physical motivation for studying this class of spaces is due to the emergence in mathematical physics during recent years of methods from algebraic geometry and Clifford and tensored division algebras. More specifically, there is the observation of Souček [Twistor Newsletter13, 22 (1981); Czech. J. Phys., Sect. B32, 688 (1982)] that the basic twistor correspondence arises in the study of the biquaternionic projective line, . In regard to the result of Souček, a subclass of the spaces presented here constitutes the -dimensional generalization of , biquaternionic projective -space, . We also discuss the generalization of the basic twistor correspondence in the more general setting of matrix projective spaces.